1. Field of the Invention
This invention relates generally to ophthalmological polarimeter systems for measuring retinal layer retardances and more particularly to an ophthalmological system for removing the effects of anterior segment birefringence from a polarimetric image of the retina.
2. Description of the Related Art
Knowing the optical characteristics of the cornea is very useful to the ophthalmologist. For example, Josef Bille describes a method and apparatus for determining optical characteristics of a cornea in U.S. Pat. No. 5,920,373. Bille describes an ellipsometer for generating a laser beam signal in a scanning tomography unit, which establishes a precise focal plane for birefringence measurements of elements in the human eye. Bille's method is procedurally and computationally intensive. Once the ellipsometer is properly focused, the laser beam emanating from the ellipsometer is selectively polarized to sequentially obtain sixteen different readings from a point in the plane of focus. These sixteen readings are then collectively used as contributions to a measurement of the birefringent property of the material at the point of focus. This process must be repeated to obtain measurements of the birefringent properties at all other image points in the plane of focus and the entire imaging procedure must be repeated to obtain the polarimetric image properties at another plane of focus.
Other practitioners concerned with corneal birefringence have also proposed various polarimetric techniques. For example, some have demonstrated the usefulness of Mueller-matrix polarimetry to assess the polarization properties of the eye.
As is well-known in the art, a general polarimeter may be used to measure the polarization properties of any optical signal, which may be expressed in terms of, for example, the Stokes vector S, which includes four components [Sj] (j=0, 1, 2, 3) that completely characterize the polarization state of an optical signal. The Stokes vector S is conventionally expressed as a four-component column vector
                    S        =                  [                                                                                                         I                                                                                        Q                                                                                        U                                                                                        V                                                              ]                        .                                              [                  Eqn          .                                          ⁢          1                ]            Components [Sj] may be characterized as simple combinations of intensity outputs from various combinations of linear or circular polarizers, where I is the total optical signal intensity, Q is the intensity difference between the horizontal and vertical linearly-polarized optical signal components, U is the intensity difference between the linearly-polarized optical signal components oriented at ±45 degrees, and V is the intensity difference between the right and left circularly-polarized optical signal components. The polarization state of any electromagnetic signal, such as a light beam, is entirely described by the four-element Stokes column vector S. Ignoring signal intensity, any Stokes vector can be located on a so-called Poincarésphere defined on the orthogonal Q, U and V axes in the manner well-known in the art.
The Mueller matrix M for a system is conventionally expressed as a 4 by 4 matrix with real elements [Mij] (i, j =0, 1, 2, 3) that contain sufficient information to describe all polarization properties of the system. Any change produced by an optical system to the polarization state S1. of an incoming optical signal may be expressed as a linear transformation (S0=M S1) of the Stokes vector for the incoming optical signal in a four-dimensional space, where M is the Mueller matrix for the optical system and SO is the Stokes vector for the outgoing optical signal:
                              S          O                =                              [                                                                                I                    O                                                                                                                    Q                    O                                                                                                                    U                    O                                                                                                                    V                    O                                                                        ]                    =                                    [                                                                                          M                      00                                                                                                  M                      01                                                                                                  M                      02                                                                                                  M                      03                                                                                                                                  M                      10                                                                                                  M                      11                                                                                                  M                      12                                                                                                  M                      13                                                                                                                                  M                      20                                                                                                  M                      21                                                                                                  M                      22                                                                                                  M                      23                                                                                                                                  M                      30                                                                                                  M                      31                                                                                                  M                      32                                                                                                  M                      33                                                                                  ]                        ⁡                          [                                                                                          I                      1                                                                                                                                  Q                      1                                                                                                                                  U                      1                                                                                                                                  V                      1                                                                                  ]                                                          [                  Eqn          .                                          ⁢          2                ]            
The usual parameters characterizing the polarizing properties of the optical system, such as retardance and reflectivity, do not appear explicitly and certain polar decomposition theorems are required to obtain physically-useful information from the Mueller matrix elements. Generally, the M00 element represents the intensity profile of the emergent beam when non-polarized light is entering the system. Elements M01, M02 and M03 describe the attenuation between two orthogonal polarization states, which is often denominated the diattenuation or dichroism (D) of the optical system. Elements M10, M20 and M30 characterize the possibility of increasing the degree of polarization of a non-polarized incident light, which is often denominated the polarizance (P) of the optical system. All Mueller matrix elements contribute to the calculation of the degree of polarization (DOP) of the optical system and the lower 3 by 3 sub-matrix elements [Mij] (i, j=1, 2, 3) alone contain information on the retardation (also denominated retardance) introduced by system birefringent structures. DOP, D and P range in value from 0 to 1 and may be expressed as closed-form functions of the appropriate Mueller matrix elements.
The birefringence of each of the various segments in the eye is assumed to be equivalent to a linear retarder and is usually expressed in terms of the retardance magnitude δ in radians (2π times the product of retarder delay time and signal frequency) and the fast-axis orientation angle θ for the segment in radians (with respect to an arbitrary horizontal basis). A linear retarder may be described by a sixteen-element Mueller matrix written in terms of retardance δ and fast-axis angle θ as follows:
                              M          ⁡                      (                          δ              ,              ρ                        )                          =                  [                                                    α                                            0                                            0                                            0                                                                    0                                                                                  c                    2                                    +                                      ks                    2                                                                                                sc                  ⁡                                      (                                          1                      -                      k                                        )                                                                                                -                  sx                                                                                    0                                                              sc                  ⁡                                      (                                          1                      -                      k                                        )                                                                                                                    c                    2                                    +                                      ks                    2                                                                              cx                                                                    0                                            sx                                                              -                  cx                                                            k                                              ]                                    [                  Eqn          .                                          ⁢          3                ]            where c=cos 2θ, s=sin 2θ, k=cos δ, x=sin δ, and α=amplitude attenuation. Note that the nine sub-matrix elements [Mij] (i, j=1, 2, 3) are sufficient to describe the polarization properties of a linear retarder. Using Eqn. 3, the total retardance δT of a sequence of two retarders with respective retardances δ1, δ2 can be shown to vary according to the relationship between the fast-axis orientation angles θ1, θ2 of the two retarders as follows:cos δT=cos δ1 cos δ2−sin δ1 sin δ2 cos 2(θ2−θ1)  [Eqn 4]Note that δT=0 when cos δ1 cos δ2=1+sin δ1 cos δ2 cos 2(θ2−θ1), showing that it is possible to “cancel” a retardance with another properly-oriented linear retarder. Two identical aligned retarders of magnitude δ (or two signal passes through a single linear retarder) is, by Eqn. 4, equivalent to a single retarder having retardance magnitude 2δ, so thatM(δ, θ) M(δ,θ)=M(2δ, θ)  [Eqn. 5]
Because the cornea is an important optical segment of the eye, the properties of in vitro mammalian corneas have been studied by practitioners in the ophthalmological art for several different purposes. For example, Bueno et al. (J. M. Bueno and J. Jaronski, “Spatially Resolved Polarization Properties for in vitro Corneas,” Ophthal. Physiol. Opt., Vol 21, pp 384-92, 2001) discuss using a Mueller-matrix imaging polarimeter in transmission mode to obtain spatially-resolved images (bitmaps) of each of the sixteen Mueller matrix elements over the cornea sample. Bueno et al. dispose a corneal sample between a polarization-state generator (PSG) and a polarization-state analyzer (PSA) each including at least one quarter-wave plate. By rotating the PSG and PSA quarter-wave plates in turn to one of four independent angular positions, sixteen independent measurements can be obtained for each pixel in a scanned image, thereby providing information sufficient for computing sixteen Mueller matrix component images of the corneal sample. A related reflective-mode procedure is employed to obtain the Mueller matrix component images of a reflective sample. Bueno et al. observe that their arrangement using sixteen independent combinations of PSG and PSA settings allows direct computation of the Mueller matrix by matrix-inversion, thereby eliminating the usual requirement for a Fourier analysis of the detected optical signal. As expected from earlier studies, Bueno et al. found the in vitro corneal retardance characteristics to vary monotonically from center to edge.
The properties of in vivo human corneas have also been studied by several practitioners in the ophthalmological art. For example, Bueno et al. (J. Bueno and P. Artal, “Double-Pass Imaging Polarimetry in the Human Eye,” Optics Letters, Vol. 24, No. 1, Jan. 1, 1999) describes a Mueller-matrix polarimeter disposed in a double-pass setup that includes two liquid-crystal variable retarders (LCVRs) and a slow scan charge-coupled device (CCD) camera. To obtain a complete set of the polarization characteristics of the in vivo human eye, three independent LCVR voltages are used to obtain nine independent polarimetric combinations. A removable quarter-wave plate is added in each leg of the polarimeter to introduce the “fourth state” necessary to complete the measurements necessary to populate the sixteen-element Mueller matrix. Later, Bueno (J. Bueno, “Polarimetry Using Liquid-Crystal Variable Retarders: Theory and Calibration,” J Opt. A: Pure Appl. Opt., Vol. 2, pp. 216-22, January 2000) describes the double-pass apparatus in more detail, including a requirement for independent calibration of each LCVR to ensure accuracy of the final Mueller matrix element images.
Bueno suggests a similar Mueller matrix polarimetry technique for examining the depolarizing properties of in vivo human corneas (Bueno, “Depolarization Effects in the Human Eye,” Vision Research, Vol. 41, pp. 2687-96, 2001), noting that the human eye presents a slight polarizing power mainly because of the presence of both circular birefringence and dichroism in the anterior segments including the cornea. Two independent rotatable quarter-wave plates (PSG and PSA) are each rotated among four positions to create the sixteen independent optical measurements necessary and sufficient to compute the Mueller matrix component images. Bueno (J. Bueno, “Indices of Linear Polarization for an Optical System,” Journal of Optics A:, Vol. 3, pp. 470-76, October 2001) also defines a pair of direct and reverse linear polarization indices to quantify deviation of the measured Mueller matrix from a perfectly linear polarizer. Nine of the Mueller matrix elements are sufficient to determine this pair of linear polarization indices.
More recently, Bueno et al. (J. Bueno and F. Vargas-Martin, “Measurements of the Corneal Birefringence With a Liquid-Crystal Imaging Polariscope,” Applied Optics, Vol. 41, No. 1, Jan. 1, 2002) provide more results of human in vivo cornea studies, suggesting that the measured variation of retardance across the pupil may result from combined effects of corneal and retinal birefringence, which are not easily separated in the living human eye. Bueno et al. use Mueller-matrix polarimetry to examine optical signals reflected from the iris. They measure a second Mueller matrix modeling the iris and use it to distinguish the iris effects from the corneal retardance data, thereby enhancing isolation of corneal birefringence from retinal birefringence. Later, Bueno et al. (J. Bueno and M. Campbell, “Confocal Scanning Laser Ophthalmolscopy Improvement by Use of Mueller-Matrix Polarimetry,” Optics Letters, Vo. 27, No. 10, May 15, 2002) suggest using the same sixteen-element Mueller-matrix polarimetry technique for confocal microscopy and specular reflection analysis.
The scanning laser polarimeter (SLP) art is described in the commonly-assigned U.S. Pat. Nos. 5,303,709, 5,787,890, 6,112,114, and 6,137,585, all of which are entirely incorporated herein by reference. The SLP is a diagnostic ophthalmological device that determines the thickness of the retinal nerve fiber layer (RNFL) by measuring the retardance magnitude and orientation angle (δN, θN) of polarized light double-passing through the RNFL layer and correlating RNFL thickness to the measured retardance (δN, θN) according to biological principles. In the eye, the anterior segment birefringence includes the combined birefringence of the cornea and the crystalline lens, and the posterior segment includes regions at the fundus. The array of nerve fibers converging from all parts of the retina to the optic nerve head is characteristically unique. Many retinal nerve fibers diverge from the fovea and curve around to converge to the optic nerve head. Within the central four or five degrees of visual field, in the fovea, other fibers, called Henle fibers, are arranged radially, like the spokes of a wheel. Both the retinal nerve fibers and the Henle fibers have “form birefringence,” with the optic axis of the birefringence parallel to the direction of the fiber. The Henle fiber retardance magnitude varies little over the normal macula.
The SLP system must segregate the effects of anterior birefringence (δC, θC) from the data to obtain the desired RNFL retardance (δN, θN) and the SLP art includes several useful methods for doing so. One method described in the above-cited patents employs a predetermined retarder (δF, θF) in the optical path to cancel a predetermined anterior segment retardance (δC, θC) in the manner suggested by Eqn. 4 above. The SLP polarimetric image provides values for the measured total retardance magnitude δT and orientation angle θT, but a single polarimetric image scan cannot resolve whether the measured orientation angle θT represents the fast-axis or the slow-axis of the total birefringence of the measured system. To resolve this “fast or slow axis ambiguity” this SLP method rotates a fixed retarder to a second orientation to obtain a second independent polarimetric scan image and determine whether the orientation measurement is the fast or slow axis, With a properly adjusted VCC, this produces a retardance magnitude δN scan image and an orientation axis θN scan image. But with a fixed anterior segment correction, the RNFL thickness measurements may be subject to significant errors arising from uncompensated anterior segment birefringence. For example, the orientation angle of corneal birefringence is known to vary among individuals, sometimes by a large angle, which may tend to mask some of the RNFL characteristics useful in identifying and diagnosing the subtle effects of certain disease processes. Another described method overcomes this disadvantage by first measuring an anterior segment retardance (δC, θC) using standard confocal polarimetry to isolate and analyze reflections from the posterior surface of the crystalline lens and then adjusting a variable corneal compensator (VCC) to approximate the retardance magnitude δF and fast-axis angle θF values necessary to cancel the measured retardance (δC, θC) in the manner suggested by Eqn. 4 above.
The commonly-assigned U.S. Pat. No. 6,356,036 B1, entirely incorporated herein by reference, discloses an improved SLP that uses post-measurement analysis of macula scan images to determine the compensation (δF, θF) necessary to cancel anterior segment retardance (δC, θC) With VCC retardance set to zero, a first SLP image is made to produce magnitude δT and orientation θT image maps of the combined anterior and posterior segment retardance over the RNFL and macula regions. An annular profile of the retardance magnitude δT is computed from an annular locus of pixels (image points) centered on the fovea in the δT image of the macula (Henle fiber layer). A single retardance value (δC, θC), representing the average anterior segment retardance (over the scan region of 2 mm or so) is derived from this annular retardance profile by assuming that the Henle fiber layer retardance (δH, θH) has a fixed magnitude δH and a radially-disposed slow-axis orientation (θH+π/2). The VCC is then set to the retardance (δF, θF) necessary to cancel the calculated anterior segment retardance (δC, θC) and a second pair of SLP image scans is made to produce a retardance magnitude δN scan image and an orientation axis θN scan image. This SLP procedure improves accuracy by using adjustable compensation and by using the Henle layer in the macula (instead of the posterior lens surface) as a reference reflection surface for measuring a (δC, θC) value representing anterior segment birefringence. This procedure assumes a healthy macula with no pathology affecting the normal optical characteristics of the Henle fiber layer.
U.S. Pat. No. 6,704,106 B2 discloses an improved SLP incorporating a residual retardance canceling system that reduces another important source of RNFL retardance measurement error by canceling the effects of residual system birefringence in the diagnostic path.
Although these SLP improvements have eliminated much of the RNFL measurement error arising from uncompensated birefringence in the measurement path, several disadvantages remain. For example, the anterior segment retardance (δC, θC) must first be measured before it can be later canceled. And the anterior segment cancellation requires the introduction or adjustment of a compensating linear retarder in the optical measurement path before repeating the RNFL imaging procedure. Moreover, each SLP retardance (δ and θ) measurement requires two independent measurements to resolve the retardance angle θ ambiguity. A first pair of scan images is needed to estimate δC and θC for the anterior segment. The VCC must then be set to cancel δC and θC before making the second pair of scan images needed to obtain RNFL retardance δN and θN, from which the desired RNFL thickness data are finally obtained. While this procedure is more efficient than the sixteen measurements required to populate an entire Mueller matrix for the RNFL image, it disadvantageously requires two complete double-scans of the retina separated by an intermediate VCC readjustment.
There is accordingly a clearly-felt need in the art for a method and system that can measure RNFL features with fewer scans for improved speed and efficiency and with the accuracy necessary for automated classification of the retinal effects of disease processes in the earlier stages. There is a particular need for a SLP system that requires neither an independent set of anterior segment retardance measurements nor the readjustment of a VCC. The unresolved problems and deficiencies are clearly felt in the art and are solved by this invention in the manner described below.